Problem: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{1}{3}-8\dfrac{7}{9} = {?}$
Answer: Find a common denominator for the fractions: $= {12\dfrac{3}{9}}-{8\dfrac{7}{9}}$ Convert ${12\dfrac{3}{9}}$ to ${11 + \dfrac{9}{9} + \dfrac{3}{9}}$ So the problem becomes: ${11\dfrac{12}{9}}-{8\dfrac{7}{9}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{12}{9}} - {8} - {\dfrac{7}{9}}$ Bring the whole numbers together and the fractions together: $= {11} - {8} + {\dfrac{12}{9}} - {\dfrac{7}{9}}$ Subtract the whole numbers: $=3 + {\dfrac{12}{9}} - {\dfrac{7}{9}}$ Subtract the fractions: $= 3+\dfrac{5}{9}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{5}{9}$